Solve for $x$ : $ 3|x - 6| - 5 = 4|x - 6| + 8 $
Answer: Subtract $ {3|x - 6|} $ from both sides: $ \begin{eqnarray} 3|x - 6| - 5 &=& 4|x - 6| + 8 \\ \\ {- 3|x - 6|} && {- 3|x - 6|} \\ \\ -5 &=& 1|x - 6| + 8 \end{eqnarray} $ Subtract $8$ from both sides: $ \begin{eqnarray} -5 &=& 1|x - 6| + 8 \\ \\ {- 8} && {- 8} \\ \\ -13 &=& 1|x - 6| \end{eqnarray} $ Simplify: $ -13 = |x - 6| $ The absolute value cannot be negative. Therefore, there is no solution.